You buy 300 shares of Qualitycorp for $30 per share and deposit initial margin of 50%. The next day, Qualitycorp's price drops to $25 per share. What is your actual margin after this price drop?

Question

BlackTom AI · Accepted Answer

Initial equity equals 50% of the purchase cost, and margin percent at any time = equity / market value.

1) Relevant concepts
- Purchase cost = number of shares × purchase price.
- Loan (borrowed amount) = purchase cost × (1 − initial margin).
- Market value after price change = number of shares × new price.
- Equity after price change = market value − loan.
- Actual margin (%) = equity / market value.

2) Step-by-step reasoning and calculations
- Purchase cost = 300 shares × $30/share = $9,000.
- Initial margin 50% → investor's equity at purchase = 0.50 × $9,000 = $4,500.
- Loan (borrowed amount) = $9,000 − $4,500 = $4,500 (this borrowed amount stays the same unless you borrow/repay).
- After price drop to $25, new market value = 300 × $25 = $7,500.
- Equity after drop = market value − loan = $7,500 − $4,500 = $3,000.
- Actual margin = equity / market value = $3,000 / $7,500 = 0.40 = 40%.

3) Intermediate steps shown above (all arithmetic shown).

4) Why 40% is correct
Because the borrowed amount remains fixed at $4,500, the decline in market value reduces your equity from $4,500 to $3,000. Dividing the remaining equity by the new market value gives 40%, so your actual margin after the drop is 40%.

5) Why the other options are incorrect
- 50%: This was the initial margin at purchase, not the margin after the price drop.
- 33%: Would correspond to equity ≈ $2,475 on a $7,500 market value; not equal to the actual $3,000 equity.
- 60%: Implies equity higher than the market value decline allows; equity actually fell, so margin cannot increase to 60%.
- 25%: Would correspond to equity ≈ $1,875; again not equal to the actual $3,000 equity.

6) Conclusion
The correct actual margin after the price drop is 40%, which matches the provided answer.

You buy 300 shares of Qualitycorp for $30 per share and deposit initial margin of 50%. The next day, Qualitycorp's price drops to $25 per share. What is your actual margin after this price drop?单项选择题

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